Indeterminate Forms and L’Hospital’s Rule

Grammar Preview

Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307. Belmont, CA: Thomson

Rewrite the following four sentences according to the cues.

Example:

Although L’Hospital did not discover L’Hospital’s Rule, the rule bears his name.

L’Hospital did not discover L’Hospital’s rule; _______________________

L’Hospital did not discover L’Hospital’s rule; nevertheless, the rule bears his name.

L’Hospital did not discover L’Hospital’s rule; in spite of this fact, the rule bears his name.

1. Although F is not defined when x = 1, we need to know how F behaves near 1.

F is not defined when x = 1; ___________________________________.

1. Although F is not defined when x = 1, we need to know how F behaves near 1.

• F is not defined when x = 1; ___________________________________.

• F is not defined when x = 1; nevertheless, we need to know how F behaves near 1.

• F is not defined when x = 1; in spite of this fact, we need to know how F behaves near 1.

2. We can’t apply the law of limits because the limit of the denominator is 0.

The limit of the denominator is 0. _____________________________________.

2. We can’t apply the law of limits because the limit of the denominator is 0.

•The limit of the denominator is 0. _____________________________________.

•The limit of the denominator is 0. Therefore, we can’t apply the law of limits.

•The limit of the denominator is 0. As a result, we can’t apply the law of limits.

•The limit of the denominator is 0. For this reason, we can’t apply the law of limits.

3. Although its limit exists, its value is not obvious.

The limit exists. ____________________________

3. Although its limit exists, its value is not obvious.

The limit exists. ____________________________

The limit exists. Nevertheless, its value is not obvious.

The limit exists. In spite of this fact, its value is not obvious.

4. Its value is not obvious because both numerator and denominator approach 0.

Both numerator an denominator approach 0. _________________________.

4. Its value is not obvious because both numerator and denominator approach 0.

Both numerator an denominator approach 0. _________________________.

Both numerator an denominator approach 0. Therefore, its value is not obvious.

Both numerator an denominator approach 0. For this reason, its value is not obvious.

Both numerator an denominator approach 0. As a result, its value is not obvious.

5. In which of the following sentences is there a condition?

a. If we have this kind of limit, then the limit may or may not exist.

b. Another situation occurs when we look for a horizontal asymptote.

c. It isn’t obvious how to evaluate this limit.

d. If the numerator wins, the limit will be ∞.

5. In which of the following sentences is there a condition?

a. If we have this kind of limit, then the limit may or may not exist.

b. Another situation occurs when we look for a horizontal asymptote.

c. It isn’t obvious how to evaluate this limit.

d. If the numerator wins, the limit will be ∞.